Paralleling two synchronous AC generators explained synchronisation and parallel operation of two generators, discussing sharing of real and reactive power.

In that discussion, the engines were speed governed, but voltage was manually controlled by adjusting excitation current. The phasor diagram showed that there is a relatively large source impedance (dominated by the synchronous reactance), EMF is around 1.5 times Vt, and terminal voltage Vt will vary widely with changes in load as a consequence.

To avoid typos, some of the text uses Python formatting of complex numbers.

Clearly there is a need in practical systems for an automatic voltage regulator (AVR) that adjusts excitation current as necessary to maintain the nominal output voltage under varying load conditions.

Common specifications of such AVRs is voltage stability within ± 0.01pu when speed is kept within ± 0.04pu.

Design and implementation of an AVR on a stand alone generator is not a huge challenge (though there are challenges), but a simple AVR that considers only the output voltage in controlling excitation is not suited to parallel machines as it will not manage sharing reactive current effectively. In fact the system is likely to be unstable with reactive load shifting back and forth between machines, and possibly unstable voltage as the AVRs interact.

There are several solutions, let’s explore a simple extension to the basic AVR that permits two identical machines to operate in parallel with good stability.

## Load sharing with quadrature droop

Recall that in the context of two parallel generators, the sharing of reactive current is determined by the excitation of both generators, and if each generator has an independent AVR (ie not cross coupled), is there a simple way to share reactive current reasonably?

Load sharing with quadrature droop is a method that allows identical machines with AVRs to operate in parallel.

Well, just as the frequency droop characteristic of the engine speed governor provides a mechanism for sharing real component of current, voltage droop can be means for sharing reactive current.

Whilst voltage droop goes against the purpose of an AVR, to share reactive current, we only need the droop to be a response to the reactive component of current to facilitate sharing of that current.

The quadrature droop method takes a voltage sample to be used for the AVR input, and adds to it a voltage proportional to the current phase shifted 90°. The block diagram of an example AVR (MX341) shows at the left four inputs, the two of interest are stator voltage sensing and droop.

Now the imaginary component of current has much stronger influence over the summed voltage, and when this boosted voltage is fed into the AVR control loop, the higher ‘sense’ voltage will tend to reduce excitation.

With two identical parallel generators, reducing excitation due to the reactive component of current will tend to reduce the share of total reactive current supplied by that machine. At the same time, the other machine is trying to reduce its share of reactive current, and the system settles with both identical machines carrying approximately equal shares, or half the total reactive current. Identical means same everything, including the set value of the AVRs.

To implement such a scheme were the reactive component of current dominates the adjustment, the AVR requires a sample of the bus voltage and a sample of the current phase shifted 90°. This is commonly achieved in three phase generators by sample the voltage Va-Vb, and using a current transformer in the c phase to sample current at 90° to Va-Vb. For this to work well, it assumes a reasonably balanced load.

A common implementation is that the droop caused by a rated current with PF=0 would be 0.05pu. This corresponds to 0.03pu droop for rated current at PF=0.8.

Above is a phasor diagram for a full load scenario where PF=0.8. It is scaled in pu.

- Phasor v is the bus voltage and zero phase reference, and is an input to the AVR;
- ji is the 90° rotated current phase of 1pu at PF=0.8;
- phasor vq is a voltage proportional to ji, and an input to the AVR (0.03+j0.04pu);
- phasor v’ is the sum of v and vq (1.030+j0.040pu), |v’|=1.03078, it is used as the process value (PV) in the AVR controller, so the boosted feedback will effectively reduce the EMF of this generator by 0.03pu;
- in a parallel machine configuration, reduction of the EMF tends to reduce the reactive current supplied, effectively sharing the reactive current with the other generator.

AVRs that support this operation can be purchased on Aliexpress for well under $100.

Of course the quadrature droop is only needed if operating in parallel. It can be disabled by shorting the sensing current transformer (never open circuit a current transformer unless it has an internal burden.) Some machine control panels have a switch to disable quadrature droop when running stand alone. AVRs will usually have some form of adjustment to calibrate the quadrature droop, ie to set the droop at some reactive current, see the operating manual for the recommended procedure.

It is really important that for effective load sharing, the speed governors have the same set value (SV), the voltage SV and quadrature droop are adjusted identically on two parallel machines to obtain close to equal sharing of the reactive current.